It was probably wool tweed. With the front-and-back bills and flaps, it anticipates cold and rainy weather, and you'd want a fabric that keeps its warmth even wet.

As the name suggests, the deerstalker is a hunting cap, and Holmes would have only worn it when outdoors in the country (or maybe during very severe weather.) Not to say that the classic illustration is wrong, only that it portrays him on one of his adventures that took him outside the city.

Don't let the wool discourage you from getting one--wear it hunting or camping when the chill sets in a little.